Acoustic resonators can be used to implement signal processing functions in various electronic applications. For example, some cellular phones and other communication devices use acoustic resonators to implement frequency filters for transmitted and/or received signals.
Several different types of acoustic resonators can be used according to different applications. For example, different applications may use bulk acoustic wave (BAW) resonators such as thin film bulk acoustic resonators (FBARs), coupled resonator filters (CRFs), double bulk acoustic resonators (DBARs), or solidly mounted resonators (SMRs).
FIG. 1A is a cross-sectional view of an example acoustic resonator 100, and FIG. 1B is a top view of acoustic resonator 100. In FIG. 1B, a line A-A′ indicates the location of the cross-sectional view shown in FIG. 1A.
As illustrated in FIG. 1A, acoustic resonator 100 comprises a piezoelectric layer 110 located between a bottom electrode 105 and a top electrode 115. The designations top electrode and bottom electrode are for convenience of explanation, and they do not represent any limitation with regard to the spatial arrangement, positioning, or orientation of acoustic resonator 100. As illustrated in FIG. 1B, acoustic resonator 100 is formed with a polygonal shape in which each side of the polygon has a different length from the other sides. This type of shape is referred to as an apodized shape, and is used to achieve desired acoustic characteristics in acoustic resonator 100. Although FIG. 1B shows only top electrode 115 with the apodized shape, other portions of acoustic resonator 100 may have a similar shape.
During typical operation, an electric field is applied between bottom and top electrodes 105 and 115. In response to this electrical field, the reciprocal or inverse piezoelectric effect causes acoustic resonator 100 to mechanically expand or contract depending on the polarization of the piezoelectric material, as indicated by an arrow in FIG. 1A. As the electrical field varies over time, an acoustic wave is generated in piezoelectric layer 110, and the acoustic wave propagates through acoustic resonator 100. For example, in some implementations, the acoustic wave propagates in parallel with the electric field as a longitudinal wave, or along the mechanical interfaces of acoustic resonator 100 as a lateral wave.
The longitudinal acoustic wave, usually called a piston mode, is electrically excited by a vertical electric field between electrode plates and has a form of laterally uniform motion with the boundaries of motion determined by an overlap of top and bottom electrodes and the piezoelectric material. Lateral acoustic waves, usually called lateral modes, are excited at the edges of the piston mode motion and facilitate continuity of appropriate mechanical particle velocities and stresses between electrically excited and non-excited regions. In general, lateral modes are specific forms of motion supported by a mechanical stack and have both longitudinal and shear components. The lateral modes can either propagate freely (so called propagating modes) or exponentially decay (so called evanescent and complex modes) from the point of excitation. These modes can be excited both by a lateral structural discontinuity (for example, at an interface between regions of different thicknesses in a membrane, or at the edge of a top or bottom electrode) or by electric field discontinuity (for example, at an edge of a top electrode where the electric field is terminated abruptly). The lateral modes generally have a deleterious impact on FBAR functionality.
For longitudinal waves, where a thickness d of piezoelectric layer 110 and of the top and bottom electrodes equals an odd (1, 3, 5 . . . ) integer multiple of half the wavelength λ of the acoustic waves, resonance states and/or acoustic resonance vibrations will occur. Because each acoustic material has a different propagation velocity for the acoustic wave, the fundamental resonance frequency for any given polarization (for example, corresponding to horizontal shear HS, thickness shear TS and thickness extensional TE lowest and higher order modes) will then be inversely proportional to a weighted sum of all thicknesses of the resonator layers.
The piezoelectric properties and, therefore the resonance properties of an acoustic resonator depend on various factors, such as the piezoelectric material, the production method, the polarization impressed upon the piezoelectric material during manufacturing, and the size of the crystals, to name but a few.
FIG. 2 is a graph illustrating a logarithmic input, impedance response versus frequency for an example acoustic resonator. As illustrated in FIG. 2, the input impedance of the example acoustic resonator exhibits a sharp negative-going (in logarithmic scale) peak from a series resonance at a lower frequency Fs, and a sharp positive-going (again, in logarithmic scale) peak from a parallel resonance at a higher frequency Fp.
FIGS. 3A through 3C are circuit diagrams illustrating electrical models of a BAW resonator such as an FBAR. The model of FIG. 3A is a modified Butterworth-Van Dyke model (MBVD) model. The frequency response of this model is a pass-band response, with frequency response for frequencies below the pass-band being attenuated by capacitances Cm and Co, and with frequency response for frequencies above the pass-band being attenuated by an inductance Lm. As illustrated in FIG. 3B, at series resistance, the BAW resonator can be modeled by a series-resonant combination of inductance Lm and capacitance Cm in series with a parasitic resistance Rs. As illustrated in FIG. 3C, at parallel resonance, the BAW resonator can be modeled by a parallel-resonant combination of inductance Lm and capacitance Co in parallel with a parasitic resistance Rp. Resistances Rs and Rp represent various heat losses and acoustic losses within the acoustic resonator.
An acoustic resonator can be employed in various types of electrical filters, such as radio frequency (RF) filters and microwave filters. In addition, acoustic resonators can be combined in various ways to produce a variety of filter configurations. The performance of an RF or microwave filter constructed with an acoustic resonator depends on the performance of the acoustic resonator, which can be expressed in terms of the resonator's parallel resistance Rp, series resistance Rs and its electromechanical coupling coefficient Kt2.
Referring to FIGS. 2, 3A, 3B and 3C, the series resistance Rs is the smallest value of magnitude of input impedance, and series resonance frequency Fs is a frequency at which that minimum occurs. The parallel resistance Rp is the largest value of magnitude of input impedance, and parallel resonance frequency Fp is a frequency at which that maximum occurs. The electromechanical coupling coefficient Kt2 is a normalized difference between parallel and series resonance frequencies Fp and Fs and is typically expressed in percent values (%) of the series resonance frequency Fs. In general, devices with higher Rp or Kt2 and lower Rs are considered to have superior performance than devices with higher Rs or lower Rp or lower Kt2. Thus, other things being equal, it is desirable to provide a filter with an acoustic resonator having a higher Rp or Kt2 and lower Rs.
An acoustic resonator can also be employed in an oscillator. Where an acoustic resonator is employed in an oscillator, the performance of the oscillator (e.g., phase noise) is affected by the Rp or Kt2 of the acoustic resonator. Moreover, as with filters, it is also desirable to provide an oscillator with an acoustic resonator having a higher Rp or Kt2 and lower Rs.
Unfortunately, many design choices that increase the Rp of an acoustic resonator tend to decrease the Kt2 of the acoustic resonator, and vice versa. In other words, there is generally a tradeoff between Rp and Kt2. Consequently, applications requiring high Rp may be required to sacrifice Kt2, and applications requiring a high Kt2 may be required to sacrifice Rp. In addition, because mechanisms determining Rp values in acoustic resonators involve scattering of multiple modes at various impedance mismatch interfaces, effectiveness of design choices to increase Rp, for example, depend on specific stack design, which is however determined by specific application of the resonator. Thus designs, frames for instance, aimed for increasing Rp may work for some acoustic stacks and may not work for the different acoustic stacks. What is needed, therefore, are acoustic resonator structures that can provide appropriate values of Rp and electromechanical coupling coefficient Kt2 according to the demands of different applications.